EP0608657A1 - Vorrichtung und Verfahren zur Verarbeitung von Formdaten zur Korrektur von Streveffekten - Google Patents

Vorrichtung und Verfahren zur Verarbeitung von Formdaten zur Korrektur von Streveffekten Download PDF

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Publication number
EP0608657A1
EP0608657A1 EP93480226A EP93480226A EP0608657A1 EP 0608657 A1 EP0608657 A1 EP 0608657A1 EP 93480226 A EP93480226 A EP 93480226A EP 93480226 A EP93480226 A EP 93480226A EP 0608657 A1 EP0608657 A1 EP 0608657A1
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Prior art keywords
shape
rectangles
exposure
increment
rectangle
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French (fr)
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Virginia Marie Chung
Joseph Blaise Frei
James Edward Stuart
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International Business Machines Corp
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International Business Machines Corp
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
    • H01J37/30—Electron-beam or ion-beam tubes for localised treatment of objects
    • H01J37/302—Controlling tubes by external information, e.g. programme control
    • H01J37/3023—Programme control
    • H01J37/3026—Patterning strategy

Definitions

  • the present invention relates to electron beam (e-beam) lithography apparatus and method and, more particularly, to performance of proximity correction of exposure patterns produced thereby to compensate exposure of a portion of a desired pattern which is in the vicinity of another portion of the desired pattern.
  • e-beam electron beam
  • Such conductive patterns are typically formed, for efficiency and general reliability regardless of the density or size of features of the conductive pattern, by applying a pattern of resist to a layer of conductive material and then etching away areas of the conductive material where resist is not present. Particularly at small sizes, patterning of the resist is typically done by exposing a layer of a resist to a pattern of radiation such as light and then removing either the exposed or unexposed portions of the resist. As feature size has decreased, different types of radiation have been used to obtain higher exposure accuracy and resolution. Exposure with charged particle beams such as electron beams has become widely used for high density integrated circuits.
  • e-beam tools In electron beam (e-beam) exposure systems, often referred to as “e-beam tools” or simply “tools”, the exposure is made by calculating the locations and sizes of portions of the desired exposure pattern.
  • e-beam tools In electron beam (e-beam) exposure systems, often referred to as “e-beam tools” or simply “tools”, the exposure is made by calculating the locations and sizes of portions of the desired exposure pattern.
  • e-beam tools e.g. interior and exterior rectangles
  • These rectangular exposure spots or spot rectangles have a maximum dimension, called a maxspot size or simply maxspot in both coordinate directions (hereinafter referred to as horizontal and vertical for convenience) and, where edge location is critical, are usually limited in dimension in one of the coordinate directions to the dimension at which best focus of the tool is obtained.
  • the other dimension of the exposure spot will usually be the full maxspot size unless a smaller spot is required.
  • Such a smaller spot is referred to as a remainder spot.
  • the technique of proximity correction referred to herein as the prior technique, method, process and the like are specifically not admitted to be prior art as to the present invention.
  • the prior technique is so identified as a matter of convenience to permit a better understanding of the invention by allowing the invention to be contrasted therewith.
  • the locations and sizes of each of the individually exposed spots are typically determined by a computer and the tool accordingly controlled thereby to develop the high speeds required in view of the extremely large numbers of spots to be written and the desired throughput of the tool.
  • Data processing requirements are reduced substantially by dividing the desired exposure pattern into rectangular portions which may each contain one or more exposure spots. Tiling of such rectangles with exposure spots in a sequential order is a very orderly procedure which can be done autonomously under computer control once the bounds of each rectangular portion are established.
  • e-beam exposure tools As with any radiation sensitive material, exposure time is cumulative. Although exposures may be readily determined and controlled in an ideal manner, an inherent problem in e-beam exposure tools is secondary emission and forward scattering (e.g. localized dispersion of the beam, measurable at the tool, as it travels to the target due to mutual repulsion of electrons in the beam, aberrations of electron lenses in the tool, variations in electron velocity and quantum effects) as well as some degree of backscattering of electrons from the resist target (or underlying structure) being exposed. At a nominal acceleration voltage of about 50 KV needed to provide an adequate e-beam current for rapid exposure of the ideal pattern, a significant further exposure occurs in the vicinity of each exposed spot due to the secondary emission and backscattering of electrons.
  • secondary emission and forward scattering e.g. localized dispersion of the beam, measurable at the tool, as it travels to the target due to mutual repulsion of electrons in the beam, aberrations of electron lenses in the tool, variations in
  • the exposure profile along the radius of the area over which secondary emission effects occur is usually highly non-linear unless adjusted by e-beam acceleration voltage as in Ban et al, U. S. Patent 4,500,789, and the exposure due to scattering effects only slightly changes the shape of the exposure distribution curve.
  • the shape of this curve may be considered to a greater or lesser degree in the proximity correction algorithm utilized to determine the actual exposure values.
  • the actual proximity correction algorithm employed is not important to the practice of the present invention.
  • U.S. patents 4,426,584 and 4,504,558 to Bohlen et al. teach aproximity corrections in a projection e-beam lithography arrangement by using multiple masks to alter exposure dose.
  • Other approaches to proximity correction are taught by U.S. Patents 4,895,760, to Nissan-Cohen, which applies windage to a pattern in accordance with multiple exposures, and 4,812,962, to Witt, which involves stepping across a pattern to identify neighboring areas of a given shape, 4,816,692, to Rudert, Jr., which is directed to a pattern splicing system, and 4,099,062, to Kitcher, which is directed to multiple overlapping exposures at reduced exposure levels.
  • the exposure of a spot may cause alteration of exposure of a second spot within the scattering exposure distance and, thus, in turn, affects the exposure of a spot beyond the scattering exposure distance.
  • the same is true for each spot rectangle in every rectangular shape in the desired pattern. In either case, the computational overhead increases enormously as the number of related exposure areas (either spots or rectangles) is increased, as is the case when spot size is reduced.
  • Exemplary known computational techniques are taught by Eichelberger et al., U. S. Patent 4,687,988, IBM Technical Disclosure Bulletin Vol. 22 No. 11, pp.5187 - 5189, Data Zoning in the Proximity-Effect Correction Technique , by M. Parikh, and Representative Figure Method for Proximity Effect Correction , by Abe et al., Japanese Journal of Applied Physics, Vol. 30, No. 3B, March, 1991, pp. L528 - L531. All of these computational techniques require either such a large quantity of data that computation cannot be efficiently done or involve simplifying assumptions which reduce the accuracy of the computational result below an acceptable level.
  • a method for partitioning shapes included in an exposure pattern including the steps of dividing the exposure pattern into shapes including interior and exterior rectangles, the exterior rectangles having a predetermined maximum width and arbitrary length, subdividing at least one of the exterior rectangles at a location along its length having the same horizontal or vertical address as the boundary of a shape in the exposure pattern which is within a scattering distance of the at least one of the exterior rectangles, and storing a description of each rectangle resulting from the subdividing step, the description including at least an address corresponding to the location, the descriptions forming an ordered list in accordance with at least one the address.
  • FIG. 1a a portion of a connection pattern as it would be formed in a device is shown in Figures 1a and 1b.
  • a corresponding ideal pattern is shown in Figure 1c with diagonal hatching showing areas of, for example, metallization. While these Figures are somewhat idealized, the patterns illustrated in Figures 1a and 1b are similar in all pertinent detail to a pattern in an actual device resulting from efforts to produce the pattern of Figure 1c and which has caused a marked reduction in manufacturing yield of that device.
  • Figures 1a and 1b correspond to precisely the same rectangle articulation and exposure data in accordance with Figure 1c. The slight difference between them has resulted from variations in processing within the normal range of acceptable manufacturing tolerances.
  • a short has been caused between wide conductor 10 (a power supply bus) and pad 12 due to the proximity therebetween.
  • Dashed circles 20 have been drawn at the nominal pattern corners of pad 12 to provide an indication of the approximate diameter of major secondary emission exposure which would occur at those points. Since spot exposures are made throughout the area of pad 12, secondary emission exposure will occur at any point of a pattern portion which is overlapped by the boundary indicated by dashed circles 20 as joined by dashed lines 22 causing proximity effects to occur.
  • Connection 14 is formed of rectangles which are preferably of only a single spot width corresponding to the best focus of the e-beam tool.
  • pad 12 must be tiled with a matrix of exposures due to its width, and blooming will occur as a function of distance from the top and bottom edges of pad 12, as illustrated. Blooming will also occur at the edge of conductor 10 inside boundary 24.
  • the blooming at 32 will be less than at 30 because of reduced proximity of connection 10 to exposure spots on the interior of pad 12 from which the secondary emission exposure will reach the edge of pad 12 but not the edge of connection 10.
  • connection 14 does not cause significant blooming since it is produced by a rectangle which is different from the rectangle used to produce pad 12 and can be separately proximity corrected.
  • connection 14 is only within the scattering radius of wide power bus 10 and thus the environment of connection 14 is substantially constant over the illustrated portion thereof.
  • the proximity effects on connection 14 due to additional exposure from pad 14 are illustrated at the radius formed by blooming at the junction of connection 14 and pad 12.
  • FIG. 2 which shows articulation of the pattern into exposure rectangles
  • no differentiation of exposure is made by division of exterior rectangle 50 formed by sleeving of conductor 10. Therefore, blooming will occur as indicated in Figures 1a and 1b.
  • the invention subdivides rectangle 50 into several smaller rectangles 50, 50' , 50'', 50''', which may be individually proximity corrected.
  • Rectangle 52 is also divided into rectangles 52' and 52'' due to proximity to the upper edge of pad 12, as illustrated.
  • the necessary proximity correction to obtain acceptable results depends to a large degree on the width of a pattern portion in a direction orthogonal to an edge since the number of spots tiled into the interior of the pattern portion within a scattering distance from an edge determines the amount of cumulative secondary emission exposure that will occur.
  • This is the direct cause of the differential blooming at 34 of Figure 1b toward conductor 10 as compared with blooming at 36 toward pad 12.
  • the formation of a connection pad which must be tiled with spot rectangles will cause multiple secondary emission exposures whereas a narrow conductor formed with a single spot rectangle across its width will cause only a single secondary emission exposure.
  • Wide conductor 10 also receives exposure correction as indicated at 56 and 56' of Figure 2.
  • the prior technique differentiates rectangles 52 and 54 even though these rectangles are portions of the same conductor since rectangle 54 is a sleeve rectangle and rectangle 52 is not.
  • the location of the division is already available as part of the data defining the location of pad 12 and thus does not increase the amount of data to be processed or require any processing in order to determine the location of such a division.
  • the formation of such a pad is relatively rare in comparison with the number of occurrences of locations where a conductor will pass within a given distance of a pad when that given distance, corresponding to the scattering distance, is several times the feature size of the pattern portion being exposed.
  • the width of conductor 10 changes as indicated at 60.
  • the boundary of exterior rectangle 62 corresponds to the boundary 64 of interior rectangle 66, indicating that no particular processing was done to locate such a division point.
  • such a division point is not optimal due to proximity to the relatively narrower portion of conductor 10 formed by interior rectangle 56 and exterior rectangles 56'. It is significant to note that at similar changes of width of conductors, which occurs quite frequently in design of conductive patterns of this type, the rectangle boundary can be optimally located without increasing the number of data which must be used during exposure in this and similar instances.
  • the invention provides a technique and arrangement to perform cutting, sorting and organizing of rectangles to greatly increase the accuracy and reduce the processing costs and nearly minimize data during compensation of proximity effects.
  • cutting of rectangles is done at several stages based on different criteria.
  • the invention is directed to a methodology of cutting, sorting and organizing rectangles and other shapes to provide an environment for a proximity correction algorithm wherein the performance of that algorithm is improved both computationally and in the pattern resulting from the e-beam exposure, regardless of the proximity correction algorithm employed.
  • Initialization of the process A00 sets initial conditions of buffers and pointers and establishes locations of rectangles which form the pattern by addresses (which, by a preferred convention, is the location of the first corner (e.g. upper left corner) of the rectangle which is encountered in a scanning pattern over the surface) and dimensions. It is assumed that sleeving, itself well known in the art, has been done and the resulting rectangles may be sorted according to whether a particular rectangle is an interior or exterior rectangle for separate storage. Generally speaking, proximity correction of interior rectangles is far less critical than for exterior rectangles since their environment (e.g. surrounding exposure areas) becomes increasingly uniform toward the center of large shapes. Therefore, it is the exterior shapes which require substantially increased processing.
  • the exterior rectangles are first sorted and preliminary cuts are made into bands to limit the extent of searching for neighbors.
  • the width of the bands is preferably chosen so that the scattering range will only extend over a relatively small number of neighboring bands. Further, at this stage, framing, which will be discussed in greater detail below, may be done and will cause further rectangles generated in the process to be stored with interior rectangles.
  • Additional cutting (A02) of the exterior rectangles is done in accordance with the flow chart of Figure 15 based on the environment of each exterior rectangle; the environment of each exterior rectangle being determined by the proximity and boundary locations of neighboring shapes.
  • This environment-based cutting of rectangles in accordance with the invention is referred to as intelligent partitioning and also provides for the recombination of some rectangles which were previously cut in order to minimize the number of rectangles which must be processed in other stages of the exposure computation process.
  • Proximity correction may then be rapidly done on the incrementally cut rectangles to determine final exposure dose for each. Recombination is then performed on the basis of calculated exposure dosages. Since recombination as well as cutting is done at several stages of the process, the processing is always limited to cuts which are likely to contribute to the optimization of the final cut positions and thus the quantity of data to be processed is reduced and the speed of the processing correspondingly increased.
  • the exterior rectangles are cut (A02), in accordance with the invention, in a manner to capture information concerning the environment of each portion of each exterior rectangle, as will be discussed in greater detail below with reference to Figures 8 - 13 and the flow chart of Figure 15.
  • This step in accordance with the invention, is referred to as intelligent partitioning and is done is a manner to ensure that the environment (e.g. the proximity to other portions of the desired pattern) is substantially constant over the extent of each of the intelligently partitioned rectangles.
  • the substantially constant environment of each of the rectangles ensures that any known proximity correction algorithm will perform substantially optimally to calculate a dose for each rectangle since any averaging done by the proximity correction algorithm will provide a more accurate exposure dose value if the averaging is done over a substantially constant environment.
  • Intelligent partitioning in accordance with the invention, also provides a tag or label, preferably stored in the form of one byte contained in each record describing a rectangle (e.g. by upper left corner location and size) until recombination is complete, for each rectangle concerning the type of cut which was made in order to reduce data volume and simplify searching during further processing.
  • Subsequent increment cutting where the cutting dimension is based on scattering characteristics and the precision of edge location required, thus initially contains and takes account of the environment since the process is performed on rectangles which have already been cut in accordance with that criterion. Increment cutting is performed on both interior and exterior rectangles to tile the rectangles with rectangular spots and is, per se, known in the art.
  • the performance of the increment cutting process (A03) is substantially improved by storing of rectangles in accordance with bands and labels, generated during intelligent partitioning (A02) to facilitate neighbor search and recombination. Therefore, the combination of intelligent partitioning with increment cutting is considered to be within the scope of the present invention.
  • all rectangles are processed through a proximity correction algorithm in the order established by the previous cutting of the intelligent partitioning which allows minimized searching for neighbors and accumulation of mutual proximity effects in order (e.g. considering only rectangles having either higher or lower addresses, depending on the direction of processing).
  • the resulting rectangles are reprocessed to recombine all adjacent rectangles which require the same exposure dose by following the labels indicating the types of cuts which were previously made which link the cut rectangles in chains.
  • Whatever proximity correction algorithm is used is nested between the processes of increment cutting and this second stage of recombination. This recombination of rectangles is based on the dose of each rectangle as computed by the particular proximity correction algorithm used and reduces the final data volume as much as possible consistent with the avoidance of blooming and loss of positional accuracy of edges.
  • recombination ultimately provides new rectangle boundaries at optimal locations which will assure optimal performance of whatever proximity correction algorithm is used.
  • the organization of the data provided by the intelligent partitioning process and increment cutting stage also enhances the speed at which the processing will be carried out since the minimum necessary volume of data will be carried forward from any stage of the process to subsequent stages of the process.
  • the process of intelligent partitioning makes cuts of rectangles at locations which approximate the locations where the rectangle enters a region within a scatter range (e.g. the secondary emission and/or scattering radius) of a portion (e.g. a corner) of another rectangle.
  • the intelligent partitioning stage may thus be rapidly done based upon the locations of edges of neighboring shapes while the final location of boundaries is based upon the cuts made during increment cutting and based on the computed exposure dose.
  • the final rectangle boundaries are automatically optimized for the proximity correction algorithm and the data for controlling exposure automatically minimized, regardless of the particular proximity correction algorithm adopted. Placement of these locations is sufficient since the additional boundary locations are reached by increment cutting within the rectangles cut by intelligent partitioning and the second stage of rectangle recombination, alluded to above.
  • Steps 702 and 704 are simply initialization steps (lumped together in Figure 19) to set up initial conditions for the remainder of the process.
  • the data structure used in the cut, sort and organize step 706 is shown in Figure 7a.
  • the band pointers, set up at 702 of Figure 6, establish a sequence and width of bands as shown in Figure 14.
  • the width of each band is preferably an integral power of two multiple of the minimum increment of the tool to be controlled.
  • Each rectangle to be processed is preferably addressable by the coordinates of at least one of its corners, as will be discussed in greater detail below. Setting the band width as an integral power of two multiple of the possible rectangle addresses allows all rectangles belonging to a band to be addressed by specifying the most significant bits of the addresses in the band and allowing all rectangles belonging to the band to be addressed as a group.
  • the initialization of output buffers 704 sets initial conditions for the system. This process also includes establishing initial conditions for the cut table list, shown in Figure 9, and entries therein as will be discussed in greater detail in regard to Figures 9 - 13.
  • the intelligent partitioning process is a major portion of the cut, sort and organize subroutine, illustrated at 706.
  • the overall function of intelligent partitioning provides a series of cuts of rectangles which partition the rectangles into regions of substantially constant pattern environment based on distances in the respective coordinate directions from neighboring shapes.
  • the rectangles are processed in a particular order and the resulting rectangles are written to output lists which are then inputted to the increment cutting stage. As a portion of this process, the resulting rectangles are organized into bands.
  • the process can merely loop 718 through successive bands, sequentially processing rectangles therein by detecting neighbors and applying a proximity correction (“Find Neighbors and Correct” 710) and locating chains of previously cut rectangles and recombining them where possible (PROX_OUT 712). Incrementing of pointers for the repeated loop 718 is performed at 714.
  • FIG 15. A detailed flow chart for the intelligent partitioning process is illustrated in Figure 15. Corresponding pseudocode will be set out below.
  • the data structure 750 comprising an entry in a cut table, as shown in Figure 7a. Such an entry is generated whenever a cut is made and describes the rectangle dimensions in a direction orthogonal to the cut. Since the cutting process proceeds in a given direction through a rectangle, two pointers are provided to indicate previous (754) and subsequent (752) cut rectangles in a chain which, in the aggregate, form the original rectangle.
  • the forward pointer corresponding to the original rectangle is changed to the location where the data for the newly created rectangle is stored.
  • the backward pointer of the newly created rectangle is set to the address corresponding to the original given rectangle.
  • the forward pointer of the newly created rectangle is set to the original forward pointer of the original given rectangle.
  • Figure 8 shows an exemplary pattern of rectangular shapes, P_RECT, A, B and C.
  • Figure 9 shows the initial conditions of a cut table entry 912 corresponding to the uncut rectangle P_RECT.
  • Dummy cut table entries 904 and 906 are preferably provided to hold pointers to entry 912.
  • the initial conditions for the P_RECT entry 912 are the locations of the left and right ends of the rectangle, R H and R L , and a default distance value preferably corresponding to the scattering range plus one. This default value facilitates the processing of comparisons and makes the process consistent throughout the intelligent partitioning process.
  • This default value essentially defines what nearby shapes will be determined to be "neighbors" for purposes of the intelligent partitioning process. If the distance is greater than this default value, no cut need be made since the nearby shape will be beyond the secondary emission radius or will receive an approximately uniform level of scattering electrons.
  • the cutting process begins at location R L specified in cut table entry 912 of Figure 9.
  • the adjacent rectangle A is found by scanning vertically from P T or P B at location R L .
  • a comparison of D A found by the scanning process, is compared to the default distance value and since, in this case, D A is smaller, the end point of rectangle A, A H , is substituted for the initial values of the end point of P_RECT, R H , and D A is substituted for the default distance as shown at table entry 914 of Figure 10.
  • a cut is simultaneously made at A H and a new cut table entry 916 is generated. The lower and upper ends of the new rectangle are set to the cut location, A H , and R H , respectively, and the default distance is maintained therein.
  • a procedure is carried out to determine the proper location of a cut table entry within the chain (e.g. to properly form the links of a linked list) for the new rectangles and whether intelligent partitioning recombinations can be made. This is done simply by proceeding through the cut table entries according to the existing pointers and comparing end points of the new cut table entry with the previous cut table entries. When the correct location is found, the pointers are moved between cut table entries to effectively insert the new cut table entry in the correct sequence in the chain. When the new cut table entry is properly located, pointers are followed to the immediately preceding and following cut table entries and the distance portions 760 compared. If the distance portions are within a predetermined distance range and equal, the adjacent cut table entries are recombined.
  • framing As the minimum feature size of a pattern is reduced below one-half of the scattering radius, it would be generally considered preferable to extend the intelligent partitioning by a process referred to as framing as a perfecting feature thereof.
  • the framing process allows dosages to be assigned which will be of increased accuracy as the edge of the shape is approached.
  • Framing is essentially a simplified form of sleeving in which large interior rectangles are cut to form four outer rectangles along the four sides of the interior rectangle and a further central rectangle fully bounded by the four frame rectangles, as shown in Figure 20 forming rectangles F, G, H and I.
  • This process can be repeated to form rectangles J, K, L and M until the total width of the frame exceeds the scattering radius although only two framings of an interior rectangle are generally done. If framing is done to correct exposure dosages of interior shapes, these rectangles are labelled as correctable shapes; otherwise they are labelled as reference shapes.
  • the width of any frame or frames can be altered by increasing spot rectangle width above the optimum e-beam tool focus toward the maxspot size if the scattering exposure contribution is sufficiently regular or uniform.
  • a combination of these two simplification techniques can also be used as dictated by the resulting increase in processing time and required precision of the process. For this reason, an increase in spot rectangle width would be preferable on second and subsequent framings of an interior rectangle.
  • the cutting or partitioning of these rectangles may be done more coarsely than with exterior rectangles since the environment is necessarily less varied because of the surrounding exterior rectangles. Therefore, scanning increments may be larger and the process accelerated accordingly.
  • the remaining central rectangle can be assigned a default exposure dose based on a final intended exposure dose or other exposure parameters. Since slight overexposure is tolerable in interior rectangles (from which framing rectangles are cut), some of these shapes may be assigned a default exposure dose corresponding to an average for the area and thus are referred to as reference shapes. As noted above, control of the edges of interior shapes is less critical and a default value can be applied at some point in the framing process. These reference shapes and the dose assigned to them is basic to the determination of the correct exposure dose for surrounding, more critical, rectangles or shapes.
  • Reference shapes may also be cut as may be convenient to reduce searching for neighboring shapes which they may affect. Reference shapes may be cut for proximity correction but only the uncut shapes are stored. The reference shapes are therefore ignored during recombination; the reference exposure dose assigned thereto being used only for dose correction.
  • the intelligent partitioning and the remainder of the process in accordance with the invention can be performed on interior rectangles, such as framing rectangles, if desired and if it is economically advantageous to do so, depending upon the computing power available and the economic considerations involved in the particular pattern and device to be made.
  • the cutting of interior rectangles is preferably nested within increment cutting since the intelligent partitioning process does not include interior rectangle data.
  • the intelligent partitioning could be performed on the remaining interior rectangle data stored after initial cutting A01 after "sleeving" the interior rectangles by repeating initial cutting A01 on the remaining data set and proceeding with a repetition of the intelligent partitioning.
  • the order in which rectangles are processed is determined by the address of the low end of the rectangle if proceeding, as assumed above, from left to right and top to bottom.
  • the pattern is also divided into bands as shown in Figure 14.
  • a data structure for containing records of rectangles belonging to each band is shown in Figure 7b.
  • Each band, as represented in this data structure contains an entry for the rectangles belonging to the band and the length of the band from the low address in the direction of the length of the band to the end of the band, as represented in storage with an end-of-band (EOB) flag. If no rectangles belong to a band, only an end of band flag will be stored.
  • EOB end-of-band
  • a sufficient number of bands are preferably provided to extend beyond the pattern by several bands which, together, exceed the scattering distance in order to provide a more consistent search pattern during the search for neighboring shapes.
  • a rectangle is treated as belonging to the band in which its upper edge falls, although this is also an arbitrary convention.
  • the height of a band is selected as an integral power of two multiple (e.g. eight, as illustrated) of the basic increment reproducible by the e-beam tool so that all rectangles belonging to a band can be accessed by using the most significant bits of the beginning address of the band and addressing the band by the uppermost address contained therein.
  • shapes are sorted by their low address corners (e.g. x and y within x).
  • the band which is termed the main band is the band currently being processed and such processing will begin with the first band which contains shapes (band 4, as illustrated.
  • band 4 contains shapes
  • shapes By the time shapes are sorted and stored into bands, they have already been subdivided based on intelligent partitioning or increment cutting or both. By storing these cut shapes into bands, it is easy to determine the maximum number of bands required to correct all shapes within the main band. Searching for neighbors and recombination are also expedited thereby.
  • the process steps from shape to shape along a primary or current rectangle to find neighbors in the order of increasing addresses until a shape is found that is beyond the scattering radius.
  • the process steps from shape to shape beginning with the lowest addressed shape that affected the previous primary shape until a shape is found that is within the scattering distance, causing cuts to be made, or a shape is found that has an address which is beyond the scattering radius from the end of the primary rectangle. This process is repeated, accumulating a measure of the mutual scattering exposure effects, until an end-of-band marker is found.
  • This label is essentially a recombination code which indicates the existence of an adjacent rectangle for possible recombination and indicates the direction (to the right or bottom) where it is to be found. All shapes above and to the right will already have been processed, reducing the number of shapes to be searched for and possibly recombined when equal exposure doses have been assigned to adjacent rectangles. It should also be noted that the data structure of Figure 7a is only used during the intelligent partitioning process and is discarded at the completion thereof. However, the cut information contained therein is saved or regenerated with information on all other cut shapes in the pattern during the process of sorting the shapes cut during both intelligent partitioning and increment cutting in the formation of the data structure of Figure 7b in which bands contain entries for cut shapes.
  • each band can be searched for abutting shapes with matching exposure doses. If the shape is not cut on the high side of either the x or the y direction, it can simply be written to an output list. If it is cut, the band table which points to the sorted shapes can be followed, recombining if the doses are the same until a different dosage assignment is found. Whenever an unmatched dose is encountered, the original shape or the combined shapes are written to the output list and the process proceeds with the following shape. This process can be done for cuts made along the vertical extent of a shape by stepping from band to band.
  • Figure 16 is basically a platform for a proximity correction algorithm, generally indicated at 1000.
  • the particular proximity correction algorithm used is unimportant to the practice of the invention other than for the requirement that the proximity correction algorithm must calculate a dose correction based on a distance separation between shapes.
  • the platform consists of a hierarchical plurality of loops which correspond to the data organization already established by the sorting and organizing functions of the intelligent partitioning process.
  • the bands are preferably processed in descending order and, within each band, shapes are processed in X-ascending, Y-descending order based on the address of the upper left corner of each shape. As noted above, this allows the accumulation of information as the process proceeds from band to band and previously processed bands need not be further considered.
  • the process illustrated in Figure 16 is repeated in its entirety, beginning at 1002 for each band of the pattern by incrementing a band pointer and initializing the start pointer (1002a), which will be incremented to find neighboring shapes, and a main pointer which identifies the shape for which neighbors are sought (1002b).
  • a test 1004 is made for an end-of-band marker which will cause branching to 1006 for repetition for a next band, looping to 1002, or ending of the process.
  • a further test 1008 is made to determine if the shape is correctable (e.g. a rectangle).
  • the process proceeds to a band loop including 1012, 1013, 1014, 1016, 1018, 1020, 1022, 1024 and 1026.
  • this band loop calculates range limits for comparison 1014 and looks at shapes in the main bands (in 1016, 1018) or in bands (initialized at step 1020) subsequent to the main band. Therefore, when a band is reached where no part of the band (which is implicit in the band address) is within the range of the current main band (determined at 1026), all shapes relevant to the main shape will have been processed in the relevant subsequent bands.
  • the process can branch 1022 to the proximity correction algorithm 1000 for calculating, adjusting and outputting dose values for the shape in the main band, looping to 1022 to accumulate corrections based on a sequence of all neighboring ("check") shapes within the calculated range. That is, within a band, if the check shape is a rectangle, as determined at 1029, the proximity correction algorithm is applied and the correction is accumulated at 1000. If the shape is not a rectangle and, hence, correctable, the proximity correction process is bypassed. Then the check shape pointer is incremented and the process loops back to 1022 for determination if the next check shape is within a range where proximity correction should be performed.
  • check all neighboring
  • this step (1026) is the last of only three numerical range comparisons which are done in the process of Figure 16.
  • Branching at 1016 rapidly steps through shapes in a band which are not within the scattering range of a main shape (e.g. the high point of the neighbor is not sufficiently close to the low point/address of the current main shape). Then, branching at 1022 occurs at the first shape in the band which is out of range above the high point of the current main shape. Similarly, branching at 1026 terminates stepping through bands at the detection of a band which is out of range. Therefore, the process can be carried out at extremely high speed based on the distance value 760 for each cut rectangle which is carried in the cut table entry. The looping sequence assures that all mutual effects of all possible pairs are accumulated. When the process has been carried out for all bands, complete, cumulative exposure dose values will have been calculated for all rectangles in the pattern or pattern portion contained within the field of the bands as illustrated in Figure 14.
  • FIG. 17 shows only the processing for a single band and must be repeated for all bands of the pattern. This branch for repeating or ending the process is done at 1102 in response to detection of an end-of-band flag or marker.
  • Steps 1104, 1105 and 1108 evaluate the types of shapes and types of cuts, if any, which have been made to produce each rectangle. If it is determined at 1104 that the shape is a reference shape and no cuts were made, the reference shape will receive a default dose and no further processing of the shape need be done.
  • the pointer is incremented at 1106 and the process loops to 1102. If the shape is not a reference shape but, instead, a proxy shape which is detected at 1105, the calculated dose is copied to the actual shape approximated by the proxy shape at 1109, a pointer is set (1109) to the address of the actual shape ("fill shape") and the dose for the actual shape is written to the data list at step 1112.
  • the shape is a rectangle which is either cut or uncut.
  • the shape is uncut subsequent to intelligent partitioning no recombination is possible since intelligent partitioning is done at points where the environment changes and it is assumed that matching doses will not be present to allow recombination. It will be recalled, in this regard, from the discussion of Figures 8 - 13 that some recombination was carried out based upon matching distances.
  • the shape is cut only at the top or left (e.g. in the direction of the low address), the shape will be the last in the ordered list of cuts and recombination will have been completed. In either case, the shape and dose may be immediately written to the data list.
  • step 1108 need test only for cuts in the direction of increasing horizontal and vertical addresses and, if such cuts are found, the abutting shape is found in step 1114 by following the ordered list of Figure 7b containing some of the data originally generated for the ordered list of the data structure of Figure 7a in which the pointer for the abutting shape will be the new start pointer for its band. If matching doses are found for the current shape and the abutting shape at step 1116, the current shape and the abutting shape are combined at 1118 and the process loops to step 1102, incrementing a pointer to the next shape at step 1106.
  • a shape is a proxy shape
  • that shape may be immediately written to a list of output rectangle data.
  • the cut was only on the left (as in rectangle 1202 of Figure 18) or top, in the preferred convention, it is known from the processing order that no other shapes can be combined with it and the shape can also be directly written to the output. If no cuts are present or cuts in more than one coordinate direction, as in cuts made in interior rectangles, it can be deduced that the shape is either not a rectangle or not an exterior rectangle. Accordingly, the shape is assigned as a reference shape, if not done earlier. A reference dose also is assigned (together with recombination based on flags or other data, as discussed above) and written to the output.
  • the band in which the adjacent rectangle falls is determined. That band is then looped through to find the corresponding shape and the exposure doses computed by the proximity correction algorithm are compared. If the doses do not match, at least within a given range, recombination is not possible and the process branches to 1106 to output the rectangle. If the doses match, and the rectangles are recombined.
  • the process then loops to 1102 but without outputting the shape being processed (now, the combined rectangle).
  • the cuts, if any, remaining in regard to this combined rectangle may indicate, when tested at 1108, in a later iteration, that no further recombination is possible and the process would branch at 1108 to 1109, 1110 and 1112 to write the combined shape to the output data list.
  • test 1108 may indicate that further recombination is possible and the process of following the forward pointer to the abutting rectangle and a comparison of exposure doses would be repeated, causing further recombination until no further cuts or an end rectangle is found or a non-matching dose causes the combined rectangle to be written to the output.
  • the pseudocode for carrying out recombination as generally illustrated in Figure 17 is as follows:
  • the process of the invention causes subdivision of a rectangle 1200 first by intelligent partitioning (A02) at cut 1201 due to shape 1200' and further division by increment cutting (A03) at 1203 and 1205.
  • the cut rectangles are maintained in a linked list as indicated by double arrows similar to Figures 9 - 13. Labels indicating the types of cuts (e.g. L, R, L&R) made are implicit in the cut table entries or can be separately maintained, if desired.
  • the cutting points specified by increment cutting also generates proximity data (e.g. d, d') in one coordinate direction which is maintained through the increment cutting process.
  • the proximity correction algorithm may assign a dose value of 98 (arbitrary units) to rectangle 1204, 95 to each of rectangles 1206 and 1208 and a dose of 92 to rectangle 1202.
  • the type of cut information is available from either the syntax of the linked list or chain of rectangles or separate storage of the same and recombination of rectangles such as 1206 and 1208 can be done when the doses compare favorably. The remaining cuts are thus shifted to optimal positions but remain based on the environment of the rectangle 1200 which is affected by shape 1200'.
  • the results of intelligent partitioning and the increment cutting are reduced by recombination based on available data and stored to memory in the smallest volume which preserves the information of interest.
  • the cuts based on environment are preserved at the conclusion of intelligent partitioning and the environment-based cuts form ends of shapes during increment cutting and thus are candidates for final cuts even though the process has only considered feature separation distances in a single coordinate direction. Since the increment cutting proceeds from the cuts made by intelligent partitioning, incremental cuts spaced at predetermined increments from the intelligent partitioning cuts assures that the remaining final cuts at changes in exposure dose will also be positioned with resolution equal to the cutting increment.
  • the position of the final cuts will also be optimized for the proximity correction algorithm used since recombination after increment cutting is based only on differences in exposure dose assigned by the proximity correction algorithm.
  • the storage of data will also be the minimum volume of data which preserves the exposure dosage computed by the proximity correction algorithm.
  • the invention provides environment-based cutting of shapes with adjustment of cuts to optimal positions while maintaining a minimum of data to be processed at all times. Since the steps of the process can be performed at very high speed, the invention provides greatly improved proximity correction at a throughput which is compatible with production processes.
  • Shape Typically, but not restricted to: rectangle, right-isosceles triangle, trapezoid, and circle.
  • Special Shape (or non-rectangle): In the illustrative implementation, any shape except a rectangle which, in the illustrative implementation, has, by far, the simplest, quickest computation of scattering effects of one shape on another. Special shapes, in the illustrative implementation include right-isoceles triangles oriented so that one or more edges are parallel to an axis of the coordinate system, and a limited set of parallelograms.
  • Proxy-Shape A rectangle which approximates an associated special-shape in area and which is centered near the center of the special-shape. It substitutes for the special-shape in all calculations of scattering effects.
  • Ref-Shape A "reference" shape which is a subdivision of a larger shape or the whole of one, which has a predetermined exposure. its presence is required for the determination of the effects of scattering from it on shapes whose exposure is being determined.
  • Main-Shape The shape in the list which, when first pointed to, has the accumulation of scattering effects from all neighbors which precede it in the list, but none of those that follow it. It remains the main-shape until scattering effects have been determined with all neighbors which follow it in the list, except that special-shapes are skipped.
  • Check-Shape A shape which comes after the main-shape in the list of shapes to be processed.
  • Start-Shape The first shape in a band to be considered as a potential neighbor to the main shape. Its identifying pointer moves along the list for the band, according to the shape's location relative to the current main-shape.
  • End-Of-Band-Marker A record that has the same format as that of a shape but has an identifying flag, and a very large coordinate along the length of the band (X, in the illustration) so that it will not be a neighbor to any "real" shape.
  • Band An ordered list (preferably physically ordered, but, optionally, a linked-list) of shapes having, except for a predetermined number of low-order bits or digits, a common coordinate of a common extremity (e.g., the corner of rectangle having the low y-coordinate). Within a band, the order is by the other coordinate of the same point and, in case of ties, then, by the value of the first coordinate. Bands are referenced from a list of pointers to the first shape in the band, or, if the contains on shapes, to an end-of-band marker.
  • Scattering-Limit The distance at which consideration of detailed computation of shape-to-shape scattering is no longer needed (some consideration of scattering among aggregates of shapes may still be appropriate). There are three relevant limits used in the method: Those on either side of the rectangle (in the "X" direction in the illustrative implementation) and the one in the direction of neighbors whose effects remain to be considered. Limiting functions may also be used when the two shapes under consideration are not directly opposite each other in any direction. This will be done when the computation of interaction is costly relative to the cost of checking the limiting function.
  • Limiting Function An approximation or calculation of boundary relative to a shape or to one or more of its extremities.
  • X_corner & Y_corner are the coordinates of the extremity.
  • Minimum_spacing is the closest two shapes can be without it being necessary to consider mutual effects of scattering individually.
  • Which side of the line a point is on can be determined by whether the sum of its coordinates is greater or smaller than the value on the right side of the equation.

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